Question

Prepare a report using the numerical methods of descriptive statistics presented in the lecture to learn how each of the variables contributes to the success of a motion picture. Make sure to include the following two items in your report.

a) Descriptive statistics for each of the four variables along with an explanation ofwhat the descriptive statistics tell us about the motion picture industry.

b) What motion pictures, if any, should be considered high-performance outliers?Explain.

Your report must include an introduction that summarizes the problem and a conclusion that addresses your findings and what you have determined from the data and your analysis.

Motion Picture	Opening Gross Sales ($millions)	Total Gross Sales ($millions)	Number of Theaters	Weeks in Release
Harry Potter and the Deathly Hallows Part 2	169.19	381.01	4,375	19
Transformers: Dark of the Moon	97.85	352.39	4,088	15
The Twilight Saga: Breaking Dawn Part 1	138.12	281.29	4,066	14
The Hangover Part II	85.95	254.46	3,675	16
Pirates of the Caribbean: On Stranger Tides	90.15	241.07	4,164	19
Fast Five	86.2	209.84	3,793	15
Mission: Impossible - Ghost Protocol	12.79	208.55	3,555	13
Cars 2	66.14	191.45	4,115	25
Sherlock Holmes: A Game of Shadows	39.64	186.59	3,703	13
Thor	65.72	181.03	3,963	16
Rise of the Planet of the Apes	54.81	176.76	3,691	19
Captain America: The First Avenger	65.06	176.65	3,715	16
The Help	26.04	169.71	3,014	30
Bridesmaids	26.25	169.11	2,958	20
Kung Fu Panda 2	47.66	165.25	3,952	18
Puss in Boots	34.08	149.26	3,963	18
X-Men: First Class	55.1	146.41	3,692	17
Rio	39.23	143.62	3,842	21
The Smurfs	35.61	142.61	3,427	20
Alvin and the Chipmunks: Chipwrecked	23.24	131.37	3,734	13
Super 8	35.45	127	3,424	16
Rango	38.08	123.48	3,923	18
Horrible Bosses	28.3	117.54	3,134	16
Green Lantern	53.17	116.6	3,816	15
Hop	37.54	108.09	3,616	11
Paranormal Activity 3	52.57	104.03	3,329	11
Just Go With It	30.51	103.03	3,548	14
The Girl with the Dragon Tattoo (2011)	12.77	102.36	2,950	12
Bad Teacher	31.6	100.29	3,049	16
Cowboys & Aliens	36.43	100.24	3,754	14
Gnomeo and Juliet	25.36	99.97	3,037	19
The Green Hornet	33.53	98.78	3,584	14
The Lion King (in 3D)	30.15	94.24	2,340	17
The Muppets	29.24	88.57	3,440	16
Real Steel	27.32	85.47	3,440	19
Crazy, Stupid, Love.	19.1	84.35	3,020	17
Battle: Los Angeles	35.57	83.55	3,417	12
Immortals	32.21	83.5	3,120	15
The Descendants	1.19	81.7	2,038	17
Zookeeper	20.07	80.36	3,482	16
War Horse	7.52	79.38	2,856	12
Limitless	18.91	79.25	2,838	16
Tower Heist	24.03	78.05	3,870	13
The Adventures of Tintin	9.72	77.48	3,087	12
Contagion	22.4	75.66	3,222	14
Moneyball	19.5	75.61	3,018	19
We Bought a Zoo	9.36	74.77	3,170	19
Jack and Jill	25	74.16	3,438	15
Justin Bieber: Never Say Never	29.51	73.01	3,118	13
Hugo	11.36	72.51	2,608	16
Dolphin Tale	19.15	72.29	3,515	18
No Strings Attached	19.65	70.66	3,050	11
Mr. Popper's Penguins	18.45	68.22	3,342	18
Happy Feet Two	21.24	64.01	3,611	16
Unknown	21.86	63.69	3,043	12
The Adjustment Bureau	21.16	62.5	2,847	12
Water for Elephants	16.84	58.71	2,820	16
The Lincoln Lawyer	13.21	58.01	2,707	18
Midnight in Paris	0.6	56.81	1,038	43
Friends with Benefits	18.62	55.8	2,926	9
I Am Number Four	19.45	55.1	3,156	15
Source Code	14.81	54.71	2,971	15
New Year's Eve	13.02	54.54	3,505	11
Insidious	13.27	54.01	2,419	23
Tyler Perry's Madea's Big Happy Family	25.07	53.35	2,288	13
Diary of a Wimpy Kid: Rodrick Rules	23.75	52.7	3,169	16
Footloose (2011)	15.56	51.8	3,555	13
The Dilemma	17.82	48.48	2,943	7
Arthur Christmas	12.07	46.46	3,376	7
Hall Pass	13.54	45.06	2,950	11
Soul Surfer	10.6	43.85	2,240	15
Final Destination 5	18.03	42.59	3,155	9
The Artist	0.2	41.36	1,756	16
The Ides of March	10.47	40.96	2,199	14
Hanna	12.37	40.26	2,545	13
Something Borrowed	13.95	39.05	2,904	12
Spy Kids: All the Time in the World	11.64	38.54	3,305	17
Scream 4	18.69	38.18	3,314	11
Big Mommas: Like Father, Like Son	16.3	37.92	2,821	14
Red Riding Hood	14.01	37.66	3,030	11
In Time	12.05	37.52	3,127	14
Paul	13.04	37.41	2,806	9
J. Edgar	11.22	37.31	1,985	15
The Roommate	15	37.3	2,534	7
Jumping the Broom	15.22	37.3	2,035	8
The Change-Up	13.53	37.08	2,913	8
30 Minutes or Less	13.33	37.05	2,888	7
Colombiana	10.41	36.67	2,614	10
Sucker Punch	19.06	36.39	3,033	9
Larry Crowne	13.1	35.61	2,976	7
A Very Harold & Kumar 3D Christmas	12.95	35.06	2,875	10
Drive (2011)	11.34	35.06	2,904	21
50/50	8.64	35.01	2,479	13
Courageous	9.11	34.52	1,214	17
The Rite	14.79	33.05	2,985	10
Arthur (2011)	12.22	33.04	3,276	9
Extremely Loud & Incredibly Close	0.07	31.76	2,630	12
The Debt	9.91	31.18	1,874	9
The Sitter	9.85	30.44	2,752	10
Priest	14.95	29.14	2,864	6

Answer 1

A) Descriptive Statistics for a variable are Mean, Std Deviation, Std Error, Min, Max, Range, Median, Mode.

n = no. of values

Mean= Average of all vales=

Std Devn =

Std Error =

Minimum = Lowst value in the sample

Max = Biggest value

Range = Max - Min

Median is the value which divides the dataset into two equal parts when arranged in ascending order.

Mode is the most recurring value in the dataset.

We find these value for each Variable

	Opening Sales
N	100
Mean	27.5142
Std Devn	26.382005
Std Error	2.6382005
Min	0.07
Max	169.19
Range	169.12
Median	19.08
Mode	#N/A

	Total sales
N	100
Mean	90.4664
Std Devn	67.78318
Std Error	6.778318
Min	29.14
Max	381.01
Range	351.87
Median	72.4
Mode	37.3

	no. of theatres
N	100
Mean	3115.35
Std Devn	608.4689
Std Error	60.84689
Min	1038
Max	4375
Range	3337
Median	3102.5
Mode	3555

	weeks in release
N	100
Mean	14.56
Std Devn	5.022589
Std Error	0.502259
Min	6
Max	43
Range	37
Median	14
Mode	16

From this we can say that for motion pictures the average opening sales is 27 million dollars, but there is a lot of discrepancies in sales for motion pictures indicated by the high std devn of 26 million dollars. While some have had opening sales as big as 170 million other has opening 0.07 millions. This means consistency is lacking in opening sales for motion picture industry. The same is reflected in total sales for movies. The Std devn for total sales is very close to the average indicating lack of consistency in sales. While no movie has recieved less than 1000 theatres for release many of them have averaged close to 3115 theatres having a modal value of 3555 and close to 15 weeks in theatre for most movies.

B) To find outliers we need to find,

th observation in the ordered data set.

, the inter quartile range

, any value lower than this would be outlier

, any value higher than this will be outlier.

For Opening Sales

Q1	13.0025
Q3	31.7525
IQR	18.75
Lower Limit	-15.1225
Upper Limit	59.8775
No. of Outliers	9

For Total Sales

Q1	39.9575
Q3	105.045
IQR	65.0875
Lower Limit	-57.6738
Upper Limit	202.6763
No. of Outliers	7

For No. of theatres

Q1	2853.75
Q3	3555
IQR	701.25
Lower Limit	1801.875
Upper Limit	4606.875
No. of Outliers	3

For weeks in release

Q1	11.75
Q3	17
IQR	5.25
Lower Limit	3.875
Upper Limit	24.875
No. of Outliers	3

Thus we can say that Opening sales in most affected by outliers.